Drawbacks of OFDM Modulation
One major drawback of the OFDM technique is inherent in the major fluctuations in amplitude of the envelope of the modulated signal and therefore in the major variations of instantaneous power.
Indeed, in the time domain, the summing of these independently modulated multiple carriers is done in terms of power most of the time but also consistently. This leads to instantaneous power peaks that can surpass the average power of the signal by more than 10 dB at certain instants.
The peak-to-average-power ratio or PAPR of the signals sent, in other words the factor characterizing the level of these power peaks relative to the average power of the signal is thus generally very high and increases with the number of carriers N.
Power amplifiers have non-linear characteristics which, coupled with the amplification of the signals, called high PAPR signals, lead to distortions: spectral regrowth of the level of the side lobes, generation of harmonics, creation of non-linear inter-symbol interference, creation of inter-carrier interference. Thus, these distortions especially give rise to errors in transmission and to a deterioration of the binary error rate (BER).
Definition of PAPR
More specifically, one particular embodiment uses a B-band OFDM signal constituted by the sum of the N regularly modulated orthogonal carriers spaced out at frequency intervals Δf such that: B=N.Δf. For a given OFDM block, each carrier is modulated by a symbol Xn belonging to a constellation (QPSK, QAM16, etc.). The inverse Fourier transform of the B-band frequency signal then gives the signal x(t) in the time domain and this signal will be transmitted. In the time domain, the duration of an OFDM block is N.Te=1/Δf, Te being the sampling period, and has the expression:
            x      ⁡              (        t        )              =                  1                  N                    ·                        ∑                      n            =            0                                N            -            1                          ⁢                              X            n                    ·                      ⅇ                          j              ·              2              ·              π              ·              n              ·              Δ              ·              f              ·              t                                            ,      0    ≤    t    <          N      ·      Te      
Assuming that the variables Xn, are random, statistically independent and centered, we deduce from this the PAPR of the OFDM signal which is expressed as:
  PAPR  =                    max                  0          ≤          t          <                      N            ·            Te                              ⁢              ·                                                        x              ⁡                              (                t                )                                                          2                            E      ·              [                                                        x              ⁡                              (                t                )                                                          2                ]            
It is noted that, with this definition of PAPR, and x(t) being the transformation from the frequency domain to the time domain, for example by an IFFT, of discrete random variables, the PAPR can become as great as N in the particular but also very rare case where {Xk}k=0N-1=1.
In practice, PAPR peaks of a given amplitude occur according to a certain probability of appearance. It is, in particular, improbable that the amplitude of the signal will be as great as N, especially as N itself will be great. Thus, classically, to characterize a PAPR of an OFDM system, the complementary cumulative distribution function (CCDF) is used. This CCDF gives the probability of the amplitude of the signal being above a certain threshold. This function is the one most used to characterize PAPR reduction systems and has the following expression:
                              CCDF          PAPR                =                ⁢                  Pr          [                                                    PAPR                ⁡                                  (                                      X                    L                                    )                                            >              γ                        ,                                                  ≈                ⁢                  1          -                                    (                              1                -                                  ⅇ                                      -                    γ                                                              )                        N                              
In practice, this equation indicates for example that the signal cannot be accurately transmitted without saturation of samples of at least one symbol in a hundred with a signal comprising 2048 carriers if the digital-analog converters and/or analog-digital converters and the power amplifiers do not work with a difference in dynamic range between average power and peak power of at least 12.2 dB, which represents an operating power ratio of 1 to 16 for the amplifier.
Below this margin, the signal will be clipped or at least highly distorted with repercussions on transmission and reception conditions.
Prior Art for the Reduction of PAPR
In the literature, many techniques have already been proposed to overcome this problem.
A common solution consists in making sure that the range of operation of the amplifier remains limited to a linear amplifier zone, thus unfortunately limiting the yield of the amplifier (a few percent instead of, classically, 50%) and therefore a major increase in the consumption of the transmitter. This is a very great constraint for the use of OFDM, especially in mobile terminals, given that the consumption of the power amplifier can represent more than 50% of the total consumption of a terminal.
A second approach is that of applying a constraint or encoding on the data sequence sent out to limit the PAPR. This method consists in building a set of code words that minimizes the PAPR. Several techniques for building these codes have been proposed. The advantage of this solution lies in the fact that it does not introduce any distortion. By contrast, the spectral efficiency is penalized without even however providing any encoding gain. In addition, to date, its field of application is limited to the OFDM modulators with small numbers of carriers N owing to an excessively great complexity of computation.
A third approach, commonly called the TI-CES technique (Tone Injection-Constellation Extension Scheme), proposes to increase the number of points of the constellations that modulate the OFDM carriers so that a point of the original constellation can have numerous corresponding possibilities of coordinates in the new constellation. According to this approach, this additional degree of freedom is used to generate a signal of lower PAPR. However, this method has numerous drawbacks owing to the fact that the extension of constellation will lead to an increase in the average power of the signal since the additional symbols have higher power levels. In addition, the selection of the best possibility of coordinates for each point requires an increase in the complexity of the computation applied, making it unsuited to hardware implementation for the real-time processing of signals.
A fourth approach, commonly called the CD (Constellation Distortion) technique, is also based on a modification of constellations and relies on the assumption that the output level of the amplification of transmission is limited by higher PAPR peaks and that, if the amplitude of these peaks can be diminished, then the emitted power can be increased. According to this technique, for a given distortion rate, a problem of optimization called a convex optimization problem is resolved in order to prepare an OFDM signal with a minimum overall PAPR level. However, this method requires a very significant increase in the average output power to compensate for the loss in terms of signal-to-noise ratio. In addition, the complexity of computation implemented increases exponentially when the constellation order becomes high.
A fifth technique, commonly called the ACE (“Active Constellation Extension”) technique is based on a modification of constellation and relies on a shift made towards greater distance from the decision axes. However, as in the above two methods, this technique is characterized by lower efficiency for the high-order constellations and by an increase in the average power of the signal, and by very high complexity of computation.
A sixth method, commonly called the TR (Tone Reservation) technique, proposes to reserve certain carriers of the OFDM multiplex which do not carry information but symbols optimized at transmission to reduce PAPR. These symbols can be optimized by using for example an SOCP (Second Order Cone Programming) type of convex optimizing algorithm. Just as in the previous method, this solution does not bring any distortion to the transmitted signal but a major drawback of this method lies in the fact that a certain number of carriers have to be reserved to make it possible to significantly reduce the PAPR. These carriers are not used to send payload information data, and this leads to a reduction of the spectral efficacy.
A seventh technique, called the “selected mapping” technique, consists in applying a phase rotation to each symbol of the sequence to be transmitted. Several phase rotation patterns can be defined. For each pattern applied to the sequence to be transmitted, operations are performed to obtain a corresponding OFDM signal and the one having the lowest PAPR is transmitted. Again, this technique provides no distortion but considerably increases complexity at transmission, since several processing operations have to be performed in parallel to then choose the most efficient one. Hence, although the other processing operations have been performed, they are not exploited. In addition, this technique makes it necessary to communicate the rotation sequence used at transmission to the receiver, and to do so with very high reliability. This leads to a reduction of spectral efficiency and a significant increase in the complexity of the system to convey the used rotation pattern applied via a dedicated channel. In addition, if this transmission is erroneous, the entire OFDM frame will be lost.
Finally, another approach is the “clipping” technique, which consists in clipping the amplitude of the signal when it goes beyond a predefined threshold. However, this clipping is by nature non-linear and introduces a distortion of the signal sent resulting not only in a degraded BER but also in a regrowth of the side lobes of the power spectral density (PSD).
In this particular context, the inventors have identified a need for a novel technique that improves the reduction of the PAPR while remaining simple to implement.